Study On The Expression Form Of "Mathematics Abstract" In Junior Middle School Education Edition Textbook

The junior high school mathematics textbook published by the People’s Education Publishing House(hereinafter referred to as the "People’s Teaching Edition")is the most basic curriculum resource,which contains rich mathematical abstract ideas.With the topic of "Study of the ’Mathematics Abstract’ Expression of The Textbook of Junior High School People’s Teaching Edition",the following three questions are studied:(1)What is the form of mathematical abstract expression in the "Mathematics Concept" of the textbook of junior high school people’s teaching edition?(2)What is the abstract expression of mathematics in the textbook "Mathematics Proposition" of junior high school people?(3)What is the abstract expression of mathematics in the textbook "number study questions" of junior high school people?Using text analysis method to study and analyze the textbooks of junior high school students,taking the four manifestations of mathematical abstraction(physical abstraction,semi-symbolic abstraction,symbolic abstraction,formal abstraction)as the framework of text analysis,according to the classification of "mathematical concept","mathematical proposition" "number learning question",statistical "number and algebra","graphics and geometry" "statistics and probability" three fields of mathematical abstract expression,combined with the training objectives of curriculum standards to reveal the distribution characteristics of mathematical abstract forms and writing intentions.And carry out differential analysis to help teachers better understand textbooks.The study found that:(1)the proportion of symbol abstraction in junior high school textbooks was up to 37.78 percent,and textbooks paid more attention to the use of symbolic abstraction to establish students’ symbolic consciousness;The proportion of formal abstraction is23.84%,and textbooks use formal abstraction to improve students’ reasoning ability and solve problems by mathematical models on the basis of symbolic abstraction.The proportion of physical abstraction is 20.27%,and textbooks form students’ sense of number,geometry and space concept through physical abstraction.The proportion of semi-symbol abstraction is18.11%,which helps students to explore the nature of mathematical objects independently.(2)The proportion of physical abstraction and symbolic abstraction in "mathematical concept" "mathematical proposition" and "number learning question" is different,that is,(1)physical abstraction and symbolic abstraction are relatively high in "mathematical concept",and the concept teaching attaches importance to the concept of situational introduction and symbolic expression;(2)"Mathematics proposition" in the semi-symbolic abstraction and symbol abstraction accounted for relatively high,proposition teaching emphasizes the students on the nature of mathematical objects,formula abstraction to build new propositions;(3)Symbolic abstraction and formal abstraction are relatively high in "number learning questions",and the teaching of exercises focuses on cultivating students’ mathematical abstraction ability to establish and solve models.(3)With the rise of the student grade,the low-level abstract expression decreases gradually,and the high-level mathematical abstract expression gradually increases.(4)"Numbers and Algebras" and "Graphics and Geometry" are important fields that embody the abstract expression of mathematics.According to the conclusion of the study,the following teaching suggestions are put forward:(1)the abstract quality of students should be trained to transform concrete examples into mathematical objects in concept teaching,(2)the abstract literacy of students using semi-symbol abstraction to extract the key attributes of research objects should be paid attention to in proposition teaching,and(3)the teaching of exercises should let students appreciate the integrity of mathematical abstract process and focus on the cultivation of formal abstraction.